A correlation-based phase unwrapping method for Fourier-transform profilometry

A new phase unwrapping algorithm based on correlation map for Fourier-transform profilometry (FTP) method is presented in this paper. It is a quality-guided phase-unwrapping method. The modulation is used as an effective parameter to indicate the reliability of the fringe image for the quality-guided phase-unwrapping method. A filtering window is introduced to calculate the modulation easily. A correlation-map function is proposed to calculate the reliability of the fringe image and to avoid choosing the width of the window in calculating the modulation. As the value of the correlation-map function is lower in areas of the local shadow and abrupt discontinuity than that in other areas, the correlation-map function is used as a guide to find the optimized phase-unwrapping path. The experimental results show that the method is feasible.     

A generalized temporal phase unwrapping algorithm for three-dimensional profilometry

A generalized temporal phase unwrapping algorithm is proposed for absolute phase measurement of object surfaces with complex topography. We first make comments on error analysis of various temporal phase unwrapping (TPU) algorithms and point out problems existing in these techniques. We present a generalized TPU algorithm (GTPU), which eliminates some limitations imposed on the fringe sequence for the classical TPU algorithms. So the desired number of fringes can be determined according to practical situation, leading to a flexible method for phase reconstruction. In addition, compared with the classical TPU algorithms, GTPU has better noise immunity and less computational complexity. Theoretical analysis and experiment results are presented to show the validity of the proposed algorithm.     

应用时域相位解包方法的三维形貌测量系统

设计一套基于时域相位解包方法的三维形貌测量系统 ,克服了传统解包方法中的误差传播效应 ,可以应用于复杂物体表面及复杂环境下的三维形貌测量。由计算机生成光栅并通过液晶投影仪投射到待测物体表面 ,用CCD摄像机采集图像并通过图像采集卡存贮到计算机中进行处理 ,实现了测量的自动化 ,完成一次高精度的测量仅需几秒钟时间。用两个特殊的人头像完成的实验证明了系统的优越性     

Gamma-distorted fringe image modeling and accurate gamma correction for fast phase measuring profilometry

In fast phase-measuring profilometry, phase error caused by gamma distortion is the dominant error source. Previous phase-error compensation or gamma correction methods require the projector to be focused for best performance. However, in practice, as digital projectors are built with large apertures, they cannot project ideal focused fringe images. In this Letter, a thorough theoretical model of the gamma-distorted fringe image is derived from an optical perspective, and a highly accurate and easy to implement gamma correction method is presented to reduce the obstinate phase error. With the proposed method, high measuring accuracy can be achieved with the conventional three-step phase-shifting algorithm. The validity of the technique is verified by experiments.     

Determination of Gabor wavelet shaping factor for accurate phase retrieval with wavelet-transform

We examined the range of shape factor of the Gabor wavelet in the analysis of spectral phase retrieval with an interferogram. We demonstrated that for the pulses with moderate high order phase the accuracy of the retrieved phase is insensitive to the shaping factor in the range of 1∼20. Both simulated ideal Gaussian spectrum and actual non-Gaussian spectrum are applied in the analysis. PACS 42.65.Re; 42.30.Rx     

最小二乘相位解包络方法

介绍一种最小二乘解相位包络的方法 ,该法的优点在于把图像作为一个整体处理 ,图像上每一个像素点的值由方程唯一确定 ,而且解得的相位图与原包裹的相位图偏差平方加权最小 ,具有局部解相法所不具有的优点。实验证明 ,它能够处理局部处理方法难以解决的相位图 ,并给出几幅实际相位图的处理结果     

Micro-phase measuring profilometry: Its sensitivity analysis and phase unwrapping

Global illumination affects shape measurement accuracy, and phase unwrapping is an important problem in phase measuring profilometry. In this paper, a micro-phase measuring profilometry is proposed to reduce the effects of global illumination. The wrapped phase error level of the proposed method is lower than that of the traditional micro-phase shifting method. First, a frequency selection rule is developed in combination with the micro-phase rule to design the frequencies of the proposed phase measuring profilometry. The frequency rule is obtained by analysing the uncertainty of the wrapped phase caused by intensity noise. Then, phase unwrapping is regarded as a congruence problem, and the closed-form robust Chinese remainder theorem algorithm is adopted to determine the correspondence. Finally, the comparative experiments are conducted on a projector-camera system. Experimental results show that the effects of global illumination can be effectively reduced with the proposed phase measuring profilometry, and the proposed frequency selection rule is valid. In addition, the performance of the robust Chinese remainder theorem in addressing the phase error is better than that of traditional Chinese remainder theorem. Furthermore, the unwrapping accuracy can nearly reach 100% if the frequency selection rule is satisfied. Otherwise, the performance degrades.     

A method for enlarging absolute phase unwrapping range by active phase setting

An active phase-setting method applied to a frequency-modulated grating is proposed for enlarging the absolute phase unwrapping range. It is found that the absolute phase unwrapping range is related to initial phase of grating. Therefore, the grating is optimized by presetting two different initial phases, which one is constant in frequency-modulation term and the other is related to the ratio of two frequency in linear phase-modulation term. By using absolute phase unwrapping algorithm, which is improved for suiting the new grating, absolute phase unwrapping range successfully is enlarged and achieves the theoretical range. The experimental results show the feasibility and validity of new method.     

Surface normal guided method for two-dimensional phase unwrapping

A novel phase unwraping method has been presented and evaluated in this paper. This method works by first constructing a quality map based on the characteristic of the active triangulation system from the wrapped phase data. The quality map is then used to guide the unwrapping. In order to reduce the execution time of phase unwrapping, we tessellate the whole wrapped phase map into blocks. Blocks with higher confidence will be unwrapped first. Experiment shows that this method can unwrap the wrapped phase map derived from the digital moiré system successfully. In data integration stage, only data with higher confidence will be reserved and used to merge together to form a complete 3D model.     

Surface normal guided method for two-dimensional phase unwrapping

A novel phase unwraping method has been presented and evaluated in this paper. This method works by first constructing a quality map based on the characteristic of the active triangulation system from the wrapped phase data. The quality map is then used to guide the unwrapping. In order to reduce the execution time of phase unwrapping, we tessellate the whole wrapped phase map into blocks. Blocks with higher confidence will be unwrapped first. Experiment shows that this method can unwrap the wrapped phase map derived from the digital moiré system successfully. In data integration stage, only data with higher confidence will be reserved and used to merge together to form a complete 3D model.     

A fast and accurate gamma correction based on Fourier spectrum analysis for digital fringe projection profilometry

In digital fringe projection profilometry, the gamma effect of the used electronic devices seriously affects the accuracy of three-dimensional (3D) topography measurements. Previous gamma correction methods do not take full advantage of the Fourier spectrum of the captured spatial-carrier phase-shifting fringe patterns. Hence, dozens of phase-shifting fringe patterns are required to carry out gamma pre-calibration. In this paper, a fast and accurate gamma correction technique based on a Fourier spectrum analysis is proposed. Only two spatial-carrier fringe patterns with different pre-encoded gamma values are needed and the number of fringe patterns required for gamma pre-calibration is significantly reduced without loss of accuracy. The proposed method is validated by experiments.     

Complex-amplitude-based phase unwrapping method for digital holographic microscopy

A complex-amplitude-based phase unwrapping approach for digital holographic microscopy is proposed in this paper. A quality map is derived directly from the reconstructed complex amplitude distribution of object wave to evaluate noise influence and phase reliability in the wrapped phase image. Quality-guided phase unwrapping algorithm is then implemented with the quality map to retrieve continuous phase profile. Unwrapping errors caused by unreliable phase data are successfully suppressed. The effectiveness of this method is demonstrated with simulation and experimental results.     

A novel optical method without phase unwrapping for subsurface flaw detection

This paper presents a novel optical method without phase unwrapping for subsurface flaw detection, based on the computer-vision reflection grating technique. In the setup, a computer-generated fringe pattern displayed on a computer-monitor is placed in front of the test object surface and forms a mirror image behind the reflective surface. The fringe pattern is perturbed according to the surface slope distribution. Unlike the current fringe pattern analysis techniques, which require one/several images, the analysis algorithm of the present method involves a sequence of fringe patterns having multiple frequencies to deduce the ‘pixel-slope’ information which is directly related to the surface slope of the test object. The novel method offers independent analysis for each pixel of the data array, and thus the problem of phase discontinuity in phase unwrapping can be eliminated. In this paper, experimental demonstration of the novel optical method to subsurface flaw detection is presented.     

基于快速傅里叶变换的四种相位解包裹算法

为了快速准确地对含有噪声的包裹相位图进行相位展开,采用理论分析与计算机模拟及实验验证相结合的方法,对基于快速傅里叶变换（FFT）的四种典型算法四次FFT算法(4-FFT)、二次FFT算法（2-FFT）、四次离散余弦变换算法(4-DCT)及横向剪切干涉与FFT相结合的算法(LS-FFT)作了对比研究。结果表明：2-FFT算法运行速度最快,4-FFT算法次之,LS-FFT算法速度最慢;4-FFT算法对含有较强噪声和轻微欠采样的实验数据的处理效果是最好的;LS-FFT算法对强噪声数据的处理效果最差。     

基于快速傅里叶变换的四种相位解包裹算法

为了快速准确地对含有噪声的包裹相位图进行相位展开,采用理论分析与计算机模拟及实验验证相结合的方法,对基于快速傅里叶变换（FFT）的四种典型算法四次FFT算法(4-FFT)、二次FFT算法（2-FFT）、四次离散余弦变换算法(4-DCT)及横向剪切干涉与FFT相结合的算法(LS-FFT)作了对比研究。结果表明:2-FFT算法运行速度最快,4-FFT算法次之,LS-FFT算法速度最慢;4-FFT算法对含有较强噪声和轻微欠采样的实验数据的处理效果是最好的;LS-FFT算法对强噪声数据的处理效果最差。     

A noise-immune method of phase unwrapping in speckle interferometry

A new phase unwrapping method that has the advantage of unwrapping of phase distribution with severe noise such as those obtained in speckle interferometry is proposed. First, computer simulations were carried out to examine the performance of the proposed method. Speckled noisy data were generated in the computer, and various types of filters having different sizes for the windows were used to carry out the phase unwrapping. It is found that the method is largely capable of phase unwrapping, and it works quite well even when the human eye cannot recognize clearly the phase jumps due to noise. Finally, the present method was applied to experimental phase distribution obtained by the speckle-shearing interferometer. The proposed method is quite simple and effective from the point of computations involved.     

Profilometry of three-dimensional discontinuous solids by combining two-steps temporal phase unwrapping,co-phased profilometry and phase-shifting interferometry

In this work we review and combine two techniques that have been recently published for three-dimensional (3D) fringe projection profilometry and phase unwrapping, namely: co-phased profilometry and 2-steps temporal phase-unwrapping. By combining these two methods we get a more accurate, higher signal-to-noise 3D profilometer for discontinuous industrial objects. In single-camera single-projector (standard) profilometry, the camera and the projector must form an angle between them. The phase-sensitivity of the profilometer depends on this angle, so it cannot be avoided. This angle produces regions with self-occluding shadows and glare from the solid as viewed from the camera׳s perspective, making impossible the demodulation of the fringe-pattern there. In other words, the phase data is undefined at those shadow regions. As published recently, this limitation can be solved by using several co-phased fringe-projectors and a single camera. These co-phased projectors are positioned at different directions towards the object, and as a consequence most shadows are compensated. In addition to this, most industrial objects are highly discontinuous, which precludes the use of spatial phase-unwrappers. One way to avoid spatial unwrapping is to decrease the phase-sensitivity to a point where the demodulated phase is bounded to one lambda, so the need for phase-unwrapping disappears. By doing this, however, the recovered non-wrapped phase contains too much harmonic distortion and noise. Using our recently proposed two-step temporal phase-unwrapping technique, the high-sensitivity phase is unwrapped using the low-frequency one as initial gross estimation. This two-step unwrapping technique solves the 3D object discontinuities while keeping the accuracy of the high-frequency profilometry data. In scientific research, new art are derived as logical and consistent result of previous efforts in the same direction. Here we present a new 3D-profilometer combining these two recently published methods: co-phased profilometry and two-steps temporal phase-unwrapping. By doing this, we obtain a new and more powerful 3D profilometry technique which overcomes the two main limitations of previous fringe-projection profilometers namely: high phase-sensitivity digitalization of discontinuous objects and solid׳s self-generated shadow minimization. This new 3D profilometer is demonstrated by an experiment digitizing a discontinuous 3D industrial-solid where the advantages of this new profilometer with respect to previous art are clearly shown.     

基于结构光编码的相展开方法

探讨了一种新的基于结构光编码相展开技术。实现方法是先将计算机构造的用于解相的光栅由投影仪投射到物体上 ,再将计算机构造的一系列黑白相间的编码光栅也由投影仪投射到物体上 ,然后将畸变栅线图像由摄像机采集到计算机中 ,用解相光栅进行解相得到折叠在 [-π ,π]区间内的相主值 ,用所述结构光编码方法进行相展开得到相位的周期 ,二者相加得到真实相位值。与传统的相展开方法相比 ,该方法相展开过程变得相对简单 ,不依赖于路径 ,不存在误差的传播 ,对噪声的抗干扰能力强 ,能够得到准确的周期 ,并能够与解相过程有机结合起来。实验证明该方法获取光栅周期快速、准确     

位相测量轮廓术中的相位修正及系统标定的新方法

介绍了在位相测量轮廓术中的一种相位修正及系统参数标定的新方法。对参考面(标定面)上点的位置_相位关系进行全场拟合,并根据该相互关系对参考面相位进行修正,能够非常有效地去除相位误差;提出的参数标定方法能精确得到投影系统参数的组合。实验证明了此方法具有良好的实用性和测量精度。     

相位编码条纹投影轮廓术的相位展开误差校正方法

相位编码法是条纹投影技术中常用的一种相位展开方法。然而,受到随机噪声、图像采样、系统离焦等因素的影响,条纹阶次与包裹相位的对应关系容易被破坏,从而引入相位展开误差。根据相位展开误差的分布特点,提出一种附加二值条纹的相位展开误差校正方法。引入的二值条纹与相位编码条纹的码字存在半周期错位,使得计算出的2组条纹阶次值具有互补性,利用两者的互补性可以有效地消除相位展开误差。仿真和真实实验均表明,该方法能够准确地恢复出被测物体的绝对相位,具有较高的可靠性。